Hello sak1987
We do have an English-speaking SBB community, which you can find here:
https://community.sbb.ch/?category.id=sbb_en
While the Half Fare Card indeed offers tickets at half fare for long-distance travel, in fare networks such as ZVV and for short distances, however, the Half Fare Card grants a reduced fare only, which can be less than half the cost of a full fare ticket.
What concerns your example is that ZVV is responsible for the pricing of your journey. You would have to contact the ZVV customer service to understand why the difference is CHF 1.20 only.
Best regards,
Roland